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Exact solutions of the one-dimensional, two-dimensional, and three-dimensional Ising models

Igor A.Stepanov

According to the traditional solutions, there is no magnetisation in the one-dimensional Isingmodel in the absence of externalmagnetic field. It is shown that there is a mistake within them. In them, local order of spins was not taken into account and the partition function and the correlation function were calculated wrongly. In this paper, that mistake is improved and a newsolution is presented.According to it, there is ferromagnetismin that model. Analogously, solutions of the two-dimensional and threedimensional Ising models are obtained.